The enormous size of the diagonal Latin squares space makes it unfeasible to enumerate all its objects straightforwardly in reasonable time. So, in order to discover the structure of this space, sophisticated search methods are needed. In RakeSearch project, we implement an application that picks up separate pairs of mutually orthogonal DLSs, which allows to reconstruct full graphs of their orthogonality.

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Processing of the square # 19 completed

Dear participants, processing of the square # 19 is fully completed! The square:

0 1 2 3 4 5 6 7 8 9 A B

1 2 0 4 5 3 8 6 7 B 9 A

2 0 1 5 3 4 7 8 6 A B 9

8 7 6 9 B A 1 0 2 5 4 3

7 6 8 B A 9 2 1 0 3 5 4

B A 9 8 7 6 5 4 3 2 1 0

5 3 4 1 2 0 B 9 A 7 8 6

9 B A 6 8 7 4 3 5 1 0 2

A 9 B 7 6 8 3 5 4 0 2 1

4 5 3 0 1 2 9 A B 8 6 7

3 4 5 2 0 1 A B 9 6 7 8

6 8 7 A 9 B 0 2 1 4 3 5

has 1228403532 orthogonal mates which would puts it on the 4th place of the rating, but another square - #17 already placed on it with equivalent number of orthogonal mates! This is very unexpected because each of the squares is a separate canonical form and cannot be converted into another square by M-transformations. But one square can be transformed into another square by rows and columns permutations. Usually this permutations break the diagonality of squares, but not in this case! Very interesting finding!

Now whole spectra of ODLS-12 globally looks like this (one point is not a single number):

Thank you for participation and donation of CPU Time!

21 Nov 2022, 20:27:05 UTC
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Processing of the square # 18 completed

Dear participants, processing of the square # 18 is fully completed! The square:

0 1 2 3 4 5 6 7 8 9 A B

1 2 0 4 5 3 8 6 7 B 9 A

2 0 1 5 3 4 7 8 6 A B 9

6 8 7 9 B A 2 1 0 5 4 3

8 7 6 B A 9 0 2 1 3 5 4

7 6 8 A 9 B 1 0 2 4 3 5

9 B A 8 7 6 5 4 3 0 2 1

A 9 B 6 8 7 4 3 5 2 1 0

B A 9 7 6 8 3 5 4 1 0 2

5 3 4 0 1 2 A B 9 6 7 8

4 5 3 2 0 1 B 9 A 7 8 6

3 4 5 1 2 0 9 A B 8 6 7

has 153240804 orthogonal mates which puts it on the 16th place of the rating which include now 4717 positions. We expected that the smallest number of orthogonal mates would correspond to this square (in comparison to other squares processed in RakeSearch) and now we see that the possible number of orthogonal mates for squares selected for processed in our project lies in the range between hundreds of millions to billions.

Now "high part" of spectra of ODLS-12 looks like this (square # 18 marked by red):

Thank you for participation and donation of CPU Time!

28 Aug 2022, 21:00:45 UTC
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Processing of the square # 17 completed

Dear participants, processing of the square # 17 is fully completed! The square:

0 1 2 3 4 5 6 7 8 9 A B

1 2 0 4 5 3 8 9 A B 6 7

2 0 1 5 3 4 A B 6 7 8 9

B 7 9 8 A 6 5 1 3 2 4 0

A 6 8 7 9 B 0 5 1 3 2 4

9 B 7 6 8 A 4 0 5 1 3 2

5 3 4 2 0 1 7 8 9 A B 6

4 5 3 1 2 0 B 6 7 8 9 A

3 4 5 0 1 2 9 A B 6 7 8

6 8 A 9 B 7 1 3 2 4 0 5

7 9 B A 6 8 3 2 4 0 5 1

8 A 6 B 7 9 2 4 0 5 1 3

has 1228403532 orthogonal mates which puts it on the 4th place of the rating among another squares with ~1.2 billion mates!

Now "high part" of spectra of ODLS-12 looks like this (square # 17 marked by red):

Thank you for participation and donation of CPU Time!

20 Jul 2022, 17:24:55 UTC
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Experiment of calculating the spectra of DLS characteristics

Dear participants!

We start a new joint search with Gerasim@Home project: calculation of spectrum of characteristics of diagonal Latin squares. As mathematical objects, DLS have various numerical characteristics. The spectrum of a characteristic is the range of values it can take. You can read about the scientific background of this new search in presentations of Eduard Vatutin: About Spectra of DLS of small orders and about Spectra of DLS of high orders and volunteer computing grid.

2 Jul 2022, 8:26:26 UTC
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Processing of the square # 16 completed

Dear folks, processing of the square # 16 is fully completed also! With you help we know, that the square:

0 1 2 3 4 5 6 7 8 9 A B

1 2 0 4 9 8 B 6 A 3 5 7

2 0 1 9 3 A 7 B 5 4 8 6

8 A 5 B 7 2 9 4 0 6 1 3

A 5 8 7 6 0 3 9 1 B 2 4

6 B 7 5 8 4 1 0 9 A 3 2

9 3 4 2 0 7 A 8 6 1 B 5

4 9 3 1 2 B 8 5 7 0 6 A

B 7 6 8 A 9 2 1 3 5 4 0

5 8 A 6 B 1 4 3 2 7 0 9

7 6 B A 5 3 0 2 4 8 9 1

3 4 9 0 1 6 5 A B 2 7 8

has 575760702 orthogonal mates which puts it on the 13th place of the rating between square with 357535322 orthogonal mates and square with 780235212 mates. And it is interesting!

Thank you for participation and donation of CPU Time!

22 Jun 2022, 11:21:10 UTC
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